ON NONLINEAR ANGULAR-MOMENTUM THEORIES, THEIR REPRESENTATIONS AND ASSOCIATED HOPF STRUCTURES

Nonlinear sl(2) algebras subtending generalized angular momentum theor ies are studied in terms of undeformed generators and bases. We constr uct their unitary irreducible representations in such a general contex t. The linear sl(2) case as well as its q-deformation are easily recov ered as specific examples. Two other physically interesting applicatio ns corresponding to the so-called Higgs and quadratic algebras are als o considered. We show that these two nonlinear algebras can be equippe d with a Hopf structure.